Structure and Dynamics of Phospholipid Nanodiscs from All-Atom and

Article pubs.acs.org/JPCB

Structure and Dynamics of Phospholipid Nanodiscs from All-Atom and Coarse-Grained Simulations Ananya Debnath*,† and Lars V. Schaf̈ er*,‡ †

Department of Chemistry, Indian Institute of Technology Jodhpur, Jodhpur 342 011, India Lehrstuhl für Theoretische Chemie, Ruhr-University Bochum, D-44780 Bochum, Germany

‡

S Supporting Information *

ABSTRACT: We investigated structural and dynamical properties of nanodiscs comprising dimyristoylphosphatidylcholine (DMPC) lipids and major scaffold protein MSP1Δ(1−22) from human apolipoprotein A-1 using combined all-atom and coarse-grained (CG) molecular dynamics (MD) simulations. The computational efficiency of the Martini-CG force field enables the spontaneous self-assembly of lipids and scaffold proteins into stable nanodisc structures on time scales up to tens of microseconds. Subsequent all-atom and CG-MD simulations reveal that the lipids in the nanodisc have lower configurational entropy and higher acyl tail order than in a lamellar bilayer phase. These altered average properties arise from rather differential behavior of lipids, depending on their location in the nanodisc. Since the scaffold proteins exert constrictive forces from the outer rim of the disc toward its center, lipids at the center of the nanodisc are highly ordered, whereas annular lipids that are in contact with the MSP proteins are remarkably disordered due to perturbed packing. Although specific differences between all-atom and CG simulations are also evident, the results obtained at both levels of resolution are in overall good agreement with each other and provide atomic level interpretations of recent experiments. Thus, the present study highlights the applicability of multiscale simulation approaches for nanodisc systems and opens the way for future applications, including the study of nanodisc-embedded membrane proteins.

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INTRODUCTION Nanodiscs (NDs) are increasingly used as a promising tool for biophysical and biochemical studies of membrane proteins.1−5 In these discoidal membrane particles, ideally two helical membrane scaffold proteins (MSPs) form a double-belt around a phospholipid bilayer patch in which a membrane protein can be embedded. Nanodiscs provide a number of advantages for functional and structural studies of membrane proteins: First, samples can be prepared that are soluble but nevertheless enable one to study membrane proteins in a native-like phospholipid bilayer. For many membrane proteins, this is beneficial over detergents, which are commonly used to mimic a membrane environment.6−8 Second, since NDs are much smaller than liposomes (a conventional alternative for functional studies in physiologically realistic membrane environments), they enable detailed structural studies by means of, e.g., cryo-electron microscopy9,10 or liquid-state NMR spectroscopy.11,12 NDs have been investigated with solid-state NMR as well,13−16 a technique for which size and solubility issues do not play a role. Third, the size as well as protein and lipid composition of NDs can be controlled by designing the MSPs from the primarily helical amphipathic apolipoprotein A-1 (apoA-1), which enables the formation of ND particles of defined size, ranging between 7−20 nm in diameter. Hence, NDs allow one to study the effects of different lipid environments and protein oligomeric states on membrane protein function.17−21 Finally, in contrast to liposomes, both © 2015 American Chemical Society

sides of the membrane proteins are accessible in NDs. In addition to these advantages for structural and functional in vitro studies, discoidal apoA-1 particles are also relevant physiologically. They are formed in the biogenesis of highdensity lipoproteins, which play a key role in lipid and cholesterol transport. Furthermore, NDs as biocompatible drug carriers have been in the focus of pharmaceutical applications.22 Most experimental studies of NDs focused on the properties of the MSPs as well as embedded membrane proteins.2,4,5 Less is known about the detailed properties of the lipids in NDs. However, these are expected to play a crucial role since the lipids constitute the direct environment of an embedded membrane protein and could thus affect its structure and/or dynamics. Recent small-angle neutron scattering (SANS) experiments of empty (i.e., no membrane protein embedded) dimyristoylphosphatidylcholine (DMPC) containing NDs have shown that the MSPs enforce a close packing of the lipids, leading to a smaller area per lipid and increased membrane thickness than in large unilamellar vesicles (LUVs).23 Accordingly, dipolar C−H lipid acyl chain order parameters, SCH, determined by solid-state NMR are significantly higher for DMPC in NDs than in liposomes, both in the liquid crystalline as well as in the gel phase.16 Fluorescence measurements Received: March 4, 2015 Revised: May 2, 2015 Published: May 15, 2015 6991

DOI: 10.1021/acs.jpcb.5b02101 J. Phys. Chem. B 2015, 119, 6991−7002

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The Journal of Physical Chemistry B

accuracy of the CG-Martini force field as well as its transferability, in particular of the lipid parameters. The rest of the article is organized as follows. In the next section, we describe the setup and details of the simulations. In the Results and Discussion section, we first describe the selfassembly of lipids and scaffold proteins into nanodiscs. We then discuss configurational entropies and order parameters of nanodisc lipids and compare them to lipids in a periodic bilayer. The simulations from the all-atom simulations are systematically compared to the CG simulations and to experimental data, where available. In addition, the lateral structure and dynamics as well as the water contacts of the lipid tails are analyzed. A Summary and Conclusions section closes this article.

showed that the steady-state anisotropy of a (9-anthroyloxy)stearic acid probe is higher and the fluorescence lifetime longer in ND membranes than in LUV membranes.23 These results suggested that the lipids in NDs experience an entropically unfavorable environment as compared to that in lamellar bilayers.23 Computer simulations allow one to directly test this hypothesis, which is inherently difficult by experiment (e.g., calorimetry can only yield the total entropy change associated with a given process but not the individual contributions, such as the configurational entropy of lipids). In addition, due to limited resolution, experimental studies could thus far not directly, i.e., at the level of individual lipid molecules, probe the different types of lipids in NDs, such as lipids located in the center of the ND versus annular lipids that are in contact with the MSPs.24,25 Complementary to experiments, molecular dynamics (MD) simulations can provide these missing detailed insights into structural, dynamic, and also thermodynamic properties of biomolecular systems, including lipids and membrane proteins.26−28 Previous all-atom (AA) MD studies of NDs and discoidal high-density lipoproteins provided detailed insight into the structure and interactions of the MSPs with themselves and with the lipids.29−39 These studies were limited to time scales of a few tens of nanoseconds or shorter, which enables one to explore the conformational space in the proximity of the starting structure or the initial stages of an onset of a relaxation process. However, these short time scales neither allow one to investigate the self-assembly and stability of NDs or their slow, large-amplitude shape fluctuations nor do they yield converged statistical ensembles. To overcome this limitation, computationally efficient coarse-grained (CG) models have been developed and employed to study ND systems on time scales up to several microseconds.40−42 In combination with a backmapping procedure to transform a particular configuration from a CG simulation into a corresponding atomistic structural ensemble,43 such CG approaches can also provide atomic-level structures that allow for a direct comparison with experimental data. All-atom and CG simulation studies have also been carried out for spherical high-density lipoprotein particles.44−49 In the present study, we combined AA- and CG-MD simulations in a sequential dual-scale setup to systematically investigate the properties of nanodisc phospholipid bilayers compared to the conventional lamellar bilayer phase. The basic idea behind this approach is to tackle the challenges due to the large system size and the slow dynamics in two stages: First, to describe the slow (multimicrosecond) self-assembly of lipids and MSPs into NDs, the efficient CG-Martini force field50−52 was used. Second, after back-mapping to atomistic resolution, subsequent all-atom MD simulations were carried out on the 500 ns time scale, yielding well-equilibrated atomistic ensembles that enable a direct comparison to recent experimental data, such as SCH lipid order parameters. The present work addresses several questions concerning simulations of NDs at different levels of resolution. First, from a biophysical perspective, what are the reasons, in terms of the underlying structural dynamics, for the experimentally observed higher acyl tail order parameters in NDs? Do lipids in NDs indeed have a lower configurational entropy than in a conventional bilayer and by how much? How do lipids located at different positions in the ND contribute to these properties? Second, from a methodological perspective, how well do the results of the CG model match those from the all-atom model? This study thus also aims at a critical, quantitative test of the

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METHODS Setup of the CG Simulation System. We first set up a simulation system comprising two MSP1 chains and 160 DMPC molecules, corresponding to the experimentally determined composition of NDs containing DMPC or DPPC lipids.1 MSP1 coordinates were obtained from the X-ray crystal structure of human apolipoprotein A1 (PDB 1AV1).53 Residues 1−22 at the N-terminus were truncated, and the Pro23Ser mutation31 was introduced. We refer to this truncated MSP1 as MSP1Δ. The atomistic MSP1 proteins were mapped into their corresponding CG-Martini representation using the martinize.py script,52 which was also used to generate the Martini version 2.2 force field topology. In this CG topology, a helical secondary structure was imposed on the entire sequence. All backbone beads were defined as N0-type CG-Martini beads, except for the charged Qd and Qa-type beads for the N- and Ctermini, respectively, and for Pro and Ala, for which C5-type beads were used. The scaffold proteins were centered in a cubic periodic box of approximately 13.5 nm, and 160 DMPC molecules were placed at random positions in the simulation box, taking care that the lipids did not overlap with each other or the scaffold proteins (Figure 1). The system was solvated with 18,812 standard Martini water beads (P4-type, one CG water bead represents four atomistic water molecules in the CG-Martini force field), and 12 sodium ions were included to neutralize the overall simulation system. The system was energy

Figure 1. CG-MD simulation of nanodisc self-assembly. Initial configuration (top: left, top view; right, side view) and final configuration after 42 μs (bottom: left, top view; right, side view). MSP1Δ monomers 1 and 2 are colored in red and blue, respectively, DMPC in green, and phosphate headgroups in orange. Lys90 residues are highlighted in yellow. Water beads are not shown for clarity. 6992


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0.12 nm grid spacing and cubic spline interpolation. After energy minimization (1000 steps steepest descent), a 20 ns NpT simulation was carried out during which harmonic position restraints were applied on all MSP heavy atoms (force constant 1000 kJ mol−1 nm−2). Temperature was kept constant at 310 K by a velocity-rescaling thermostat55 with a coupling constant of 0.5 ps. For constant 1 bar pressure, isotropic Berendsen pressure coupling was applied with a 2 ps coupling time constant and compressibility 4.5·10−5 bar−1. Finally, position restraints were switched off, and 500 ns NpT MD simulations were carried out. For the periodic bilayer, semi-isotropic pressure coupling was used, as described for the CG-MD simulations above. Analysis. Coordinates were saved to disk every 100 and 500 ps for the AA and CG simulations, respectively. Unless otherwise noted, the reported results were obtained from analyzing the last 400 and 2000 ns of the AA and CG simulations, respectively. Configurational Entropies. To estimate the configurational entropies of the lipid acyl chains, we used the quasi-harmonic approximation as formulated by Schlitter.66 We followed the procedure described by Baron and co-workers67,68 and calculated the entropy build-up over time. The Schlitter approximation provides an upper bound to the true configurational entropy,

minimized by 1000 steepest descent steps prior to MD simulation. CG-MD Simulations. All MD simulations were carried out with Gromacs (version 4.5.5).54 First, the energy-minimized system was simulated for 1 ns with a 2 fs integration time step in the NVT ensemble. This was followed by 42 μs (plain, i.e., unscaled simulation time, see below) of CG-MD in the NpT ensemble with a 20 fs integration time step. To keep the temperature constant at 303 K, the velocity rescaling thermostat of Bussi and co-workers55 was applied, with a coupling time constant of τT = 1 ps. Isotropic Berendsen pressure coupling was used to maintain 1 bar pressure, with a 4 ps coupling time constant and a compressibility of 3·10−5 bar−1. Lennard-Jones (6,12) and Coulomb potentials were smoothly shifted to zero from 0.9−1.2 nm and 0−1.2 nm, respectively. The bead-based nonbonded pair list was updated every 10 steps within a 1.4 nm search radius. For reference, we also simulated an infinite (periodic) DMPC bilayer, comprising 128 lipids (64 in each leaflet) solvated by 2000 CG water beads. This CG-MD simulation was carried out for 2 μs in the NpT ensemble with simulation parameters as described above for the ND systems, with the exception that semi-isotropic pressure coupling was applied by separately coupling the lateral (xy) and normal (z) dimensions of the periodic box to a pressure bath. Backmapping and All-Atom MD Simulations. To obtain starting structures for the subsequent all-atom MD simulations, the final snapshots obtained from our CG-MD simulations (of both the 160-DMPC nanodisc and the 128DMPC periodic bilayer) were transformed into an atomistic representation using a recent backmapping algorithm, as implemented in Gromacs version 3.3.1.56 During the CG-toAA resolution transformation, the systems were linearly cooled down from an initial temperature of 1300 K to the desired target temperature of 310 K during 100 ps of simulated annealing (SA). During the SA, which was carried out in the NVT ensemble, the atomistic particles were connected to their corresponding CG beads (according to the AA-to-CG mapping) through harmonic potentials. No constraints were applied, and an integration time step of 1 fs was used. To control the temperature, stochastic coupling (SD integrator in Gromacs) with an inverse friction constant of τT = 0.1 ps was applied. For the resolution transformation simulations, the Gromos 43A2 protein force field57 was used, together with the Berger united atom force field58 for the DMPC lipids. The final backmapped structures, which comprised ca. 240,000 atoms for the ND system and ca. 30,000 atoms for the 128-DMPC periodic bilayer, were taken as starting structures for the subsequent all-atom MD simulations. In these simulations, we switched to the Amber99SB-ILDN protein force field.59,60 The DMPC lipids were described with the Berger force field in a format compatible with the Amber protein force fields.61 The TIP3P62 water model was used. SETTLE63 was used to constrain the internal degrees of freedom of the water molecules and LINCS64 to constrain all other bonds. Together with the use of virtual interaction sites for the protein hydrogens, this allowed for an integration time step of 4 fs. Short-range Coulomb and Lennard-Jones (6,12) interactions were cut off at 1.0 nm. Analytical dispersion corrections were added to energy and pressure to correct for the truncation of the Lennard-Jones interactions. The nonbonded pair list was updated every 20 fs. Long-range Coulomb interactions were treated with the particle-mesh Ewald (PME) method65 with a

S=

⎞ ⎛ kB k Te 2 ln det⎜1 + B 2 M1/2CM1/2⎟ > Strue 2 ℏ ⎠ ⎝

where kB is the Boltzmann constant, T the temperature, e Euler’s number, ℏ the Planck constant, and M the 3Ndimensional diagonal mass matrix for the N particles. C is the covariance matrix of particle fluctuations, C = ⟨(x − ⟨x⟩) (x − ⟨x⟩)T⟩, where the 3N-dimensional vector x represents the Cartesian coordinates of the N particles for which the entropy is calculated after fitting to a reference structure. Averaging was carried out over all individual lipid molecules and trajectory frames. The initial configuration of the production simulations was used as a reference structure for the least-squares fit of successive trajectory configurations to remove the overall translational and rotational motion of each lipid. The influence of this choice was tested by using an idealized energyminimized all-trans lipid configuration for the fit, which yielded identical results within the margins of the statistical error. The covariance matrix was calculated for the particles of both the sn1 and sn2 acyl tails of a lipid molecule, including the carboxylic acid ester groups. For the CG DMPC lipids, which comprise 10 CG beads (2 charged beads for the zwitterionic PC headgroup, 2 polar beads for the ester linkage, and 3 apolar beads for each acyl tail), the ester linkage beads were included in the calculation of C, i.e., each tail comprises 4 CG beads. For both AA and CG entropies, the same set of particles that was used to calculate C was also used for the least-squares fit. Thus, the calculated entropies can be referred to as internal (since translation and rotation are removed) two-tail entropies. Our approach has two principal limitations. First, the quasiharmonic approximation overestimates the true entropies due to the neglect of anharmonicities and correlated motions. Second, the entropy of the entire bilayer is not the sum of the entropies of the individual lipid molecules because of intermolecular correlations. However, these limitations are not of major concern for this study because our focus is on entropy differences between the lipids in a nanodisc and in a 6993


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conformation into a more circular belt-like conformation. Those lipids that failed to get rapidly incorporated into the center of the MSPs assemble into small micellar aggregates, which diffuse through the simulation box until they finally encounter the ND and fuse with it. To characterize the course of the self-assembly process, Figure 2 shows the number of

conventional periodic bilayer, where these effects can be expected to largely cancel out. Acyl Chain Order Parameters. Order parameters, defined as P2 = 0.5⟨3 cos2 θ −1⟩, were calculated from the MD trajectories. The angular brackets denote time and ensemble averaging. Two different types of order parameters were analyzed. From the all-atom simulations, SCH order parameters were obtained. In this case, θ is the angle between the C−H bond vector and a reference axis, in our case the bilayer normal. To calculate SCH from our MD simulations with the unitedatom lipid force field, in which no explicit hydrogens are present, the C−H bond vectors were reconstructed based on the positions of the neighboring carbon atoms in the acyl chain. These SCH order parameters can be directly compared to those obtained from solid-state NMR for DMPC nanodiscs.16 From the CG simulations, we calculated P2 for the CG bonds in the lipid acyl chains, i.e., in this case θ is the angle between the bond vector between two neighboring CG beads and the bilayer normal. To enable a direct comparison of AA and CG simulations, P2 order parameters were also calculated from the AA simulations after transforming the AA trajectory into the CG representation, employing the AA/CG mapping defined by the Martini force field. Before calculating order parameters from the nanodisc simulations, the ND was first aligned along its principal axis such that the bilayer normal corresponded to the z-axis. Then, trajectory frames were successively fitted onto this reference structure to remove overall translation and rotation of the ND. To distinguish between the different types of lipids in the nanodisc, the individual lipid molecules were dynamically indexed based on their radial positions. We categorized the lipids into three classes, referred to as central, intermediate, and annular. A lipid was assigned as central if its center of mass was within a region of radius 2 nm with respect to the center of mass of all lipids in the ND. Lipids within a shell between 2 and 3.5 nm radius are referred to as intermediate, and all other lipids as annular; the latter are neighboring the scaffold proteins. Lateral Diffusion. To characterize the lateral mobility of the lipids, the 2-dimensional mean square displacements (MSD) of the DMPC molecules in the bilayer plane, ⟨|r(t0 + t) − r(t0)|2⟩, were calculated from the aligned and fitted trajectories (see above). Here, r is the center of mass vector of the molecule, and the ensemble averaging includes all lipids. Time window averaging was carried out over all time origins t0. To analyze the nonlinear dependence of the MSD on time, MSD ∝ tα, the exponent α was calculated from the local slope of the MSDover-t curves, α = d(ln MSD)/d(ln t), with 5 ns intervals used for the linear fits.

Figure 2. Self-assembly of DMPC lipids into a nanodisc. A lipid was considered part of the nanodisc (i) if any of its beads was within 4.5 nm of the center of mass of all lipids, and (ii) none of its beads was located outside a slab of thickness 5 nm along the z-dimension, centered on the nanodisc (the ND was oriented in the xy-plane for this analysis). Lipids trapped between the two MSP1Δ chains were not counted as part of the ND.

DMPC lipids that assemble into the nanodisc over time. After the initial sharp increase due to the collapse and rapid incorporation of the lipids into the MSP1Δ scaffold, the stepwise increase at 7.5 μs is caused by the fusion of the last remaining DMPC micelle with the ND. From this point in time onward, all DMPC molecules were incorporated into the confined space encircled by the scaffold proteins. However, the nanodisc did at this stage not yet adopt an ideal discoidal shape because a few DMPC molecules were trapped in between the two protein chains, protruding their headgroups outward into the water. As a consequence, the lipid headgroup density profiles along the bilayer normal were asymmetric. These trapped lipids did not rearrange on the CG-MD simulation time scale. Thus, to ensure the formation of a proper ND, we stopped the simulation after 16 μs and translated the trapped DMPC molecules toward the center of the ND, taking care to have the same number of lipids in each leaflet. After energy minimization, the CG-MD simulation was continued for 12 μs, after which the symmetrization procedure was repeated. The final 14 μs of simulation eventually yielded an ideal discoidal nanodisc, in which the periphery of the bilayer formed by the DMPC lipids is enclosed by the MSP1Δ proteins in a doublebelt fashion (Figure 1). Next, to study the properties of the final self-assembled nanodisc at the fully atomistic level, we converted the final snapshot of the CG-MD simulation into a corresponding atomistic configuration. Figure 3a shows the ND after the subsequent 500 ns all-atom MD simulation. Overall, the structure of the ND is stable during the all-atom MD, as evidenced by the stable helical structure of the scaffold proteins (helicity 80%, averaged over the last 100 ns of the simulation and all residues of the two MSP1Δ proteins). The secondary structure plot in Figure 3b shows that both MSP1Δ chains (178 residues each) comprised repeating helical stretches interrupted by short coils or turns. The high degree of helicity of the scaffold proteins is consistent with the current consensus picture supported by theoretical and experimental data,

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RESULTS AND DISCUSSION Scaffold Proteins and Lipids Spontaneously SelfAssemble into a Stable Nanodisc. The self-assembly of the lipids and scaffold proteins into a nanodisc occurs on a multimicrosecond time scale and was thus studied at the CG level. Figure 1 shows the initial and final configurations of the 160-DMPC nanodisc CG-MD simulation. In the initial (X-ray crystal) structure, the two MSP1Δ chains are aligned on top of each other, forming an eight-shaped ring with Lys90 from both chains juxtaposed (yellow spheres in Figure 1). Within the first 2−3 μs of the simulation, many DMPC lipids get enclosed by the MSP1Δ ring and start to form a bilayer. During this time, the MSP1Δ scaffold changes from the eight-shaped initial 6994


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Figure 3. (a) Snapshot (after 500 ns) of all-atom simulation of a nanodisc (left, top view and right, side view). (b) Secondary structure (definition according to DSSP84). Residues 1−178 and 179−356 correspond to MSP1Δ monomers 1 and 2, respectively. Color code: α-helix, blue; turn, yellow; bend, green; coil, white.

Figure 4. Lipid acyl tail configurational entropies from (a) AA and (b) CG simulations, averaged over all DMPC molecules. The entropy is slightly lower in the ND than in the bilayer. The entropy in the bilayer converges faster than that in the ND. The error bars (smaller than the size of the symbols) reflect the standard error of the mean, which was derived under the assumption that all individual lipids are independent. The estimated statistical errors are 2.4 and 1.2 J mol−1 K−1 for the all-atom ND and bilayer, respectively. For the CG systems, the statistical errors are well below 1 J mol−1 K−1.

including the X-ray crystal structures.53,69 In addition, our allatom MD simulations validate one of the major assumptions underlying our CG-MD approach, which is the assumed helical secondary structure of the scaffold proteins. Nanodisc Lipids Have Lower Entropies. Figure 4 shows the buildup of the configurational entropy of the DMPC acyl chains over time for both the nanodiscs as well as the periodic bilayer. Both at the all-atom (Figure 4a) as well as the CG level (Figure 4b), entropy build-up is slower, and the values approached in the long time limit are lower in the ND than in the periodic bilayer. The entropy difference between the ND and bilayer, ΔSconfig, is small but significant. The AA simulations (Figure 4a) yield ΔSconfig = 29 J mol−1 K−1, which results from the limiting values (after 400 ns) of 1908 and 1879 J mol−1 K−1 for the bilayer and ND, respectively (Table 1). At the CG level, the entropy difference between the ND and bilayer is smaller, only 10 J mol−1 K−1(Figure 4b). This smaller entropy difference results from much smaller absolute values. In the long time limit, the CG configurational entropies are 642 and 632 J mol−1 K−1for the bilayer and ND, respectively. The magnitudes of Sconfig necessarily differ between the AA and CG levels due to the different number of particles. This intrinsic difference in Sconfig is in the current case a factor of 3, in agreement with the observation that also ΔSconfig is 3 times smaller at the CG than at the AA level. Taken together, we conclude that the CG-Martini force field successfully, albeit not quantitatively, picks up the intricate differences between the configurational ensembles that underlie the different lipid acyl chain configurational entropies in nanodiscs and conventional bilayers. Furthermore, comparing the AA and CG entropy build-up curves allows one to assess the convergence of the estimated entropies. Indeed, due to the slow conformational sampling, the all-atom entropies have not yet fully reached a plateau value after 400 ns (Figure 4a). This uncertainty is also reflected in the statistical errors, which in the ND is larger because of the heterogeneity of the ensemble due to the differential acyl chain

Table 1. Comparison of Lipid Acyl Tail Configurational Entropies and Order Parameters in the Nanodisc and Periodic Bilayera property −1

−1

Sconfig (AA-MD) [J mol K ] Sconfig (CG-MD) [J mol−1 K−1] SCH (AA-MD) SCH (ss-NMR)16 a

nanodisc

bilayer

1879 632 0.188 0.260

1908 642 0.166 0.172

Order parameters are averaged over the entire sn1 and sn2 tails.

order depending on the radial position of the lipids in the ND (see below). Nevertheless, extending the AA-MD simulations by another 50 ns changed the limiting values of Sconfig by only 1 and 2 J mol−1 K−1 for the periodic bilayer and ND, respectively, demonstrating that the estimated entropies are statistically accurate. At the CG level, sampling of acyl chain configurations is close to complete, and the entropies are well converged within less than 0.5 μs (Figure 4b). It is tempting to assume that the all-atom entropies should converge on a similar time scale. However, this is not the case, since sampling is considerably faster at the CG level. For aliphatic hydrocarbon chains in the liquid phase, configurational entropy build-up is faster by a factor of ca. 4 in the Martini model as compared to a united-atom fine-grained model.67,68 Hence, assuming that a similar time-conversion factor applies in the present case, the AA entropies are expected to fully converge only after ca. 2 μs, which represents a very large computational effort given the system size of ca. 240,000 atoms. However, the CG-MD simulations clearly demonstrate that the entropy difference between ND and periodic bilayer persists even in the long time 6995


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The Journal of Physical Chemistry B limit. Thus, we conclude that the observed entropy difference at the intermediate time scales accessible to the all-atom simulations is not due to insufficient sampling. The exhaustive sampling at the CG level is also evident from the lateral mean square displacements of the lipids, see below. In summary, our calculations of the configurational entropy as a measure for the accessible configurational space show that the entropy of the lipid acyl tails is lower in the nanodisc due to the confinement by the surrounding scaffold proteins. The difference of ΔSconfig = 29 J mol−1 K−1 (obtained at the AA level) may seem small but corresponds to a non-negligible contribution of TΔSconfig = 8.7 kJ mol−1 to the free energy at 300 K. Our results are in qualitative agreement with and provide a basis for a molecular interpretation of time-resolved SANS experiments,23 which showed that the activation entropy for lipid desorption from NDs is favorable, whereas it is unfavorable for large unilamellar vesicles. Lipid Order Parameters Are Higher in Nanodiscs. Order parameters are a measure of the orientational mobility and anisotropy of the lipid hydrocarbon segments along the acyl tail. Here, we have adopted three slightly different approaches to analyze order parameters. First, to enable a direct comparison with NMR experiments,16 we have calculated the acyl chain SCH order parameters from our all-atom MD simulations. Second, in addition to the overall SCH, i.e., averaged over all lipids, we also analyzed the order parameters as a function of the radial position in the ND, revealing substantial heterogeneity−in terms of the configurational distributions−of the different types of lipids in the ND. Third, to quantitatively compare the AA and CG results, P2 order parameters of the bonds between CG beads in the acyl tails were analyzed. To enable this latter comparison, the AA trajectories were analyzed in terms of their CG coordinates. Figure 5a and Table 1 compare the order parameters obtained from solid state NMR16 and our simulations. For the tensionless periodic bilayer, the agreement between NMR- and MD-derived order parameters is excellent. Averaged over the entire acyl chain, SCH is 0.166 and 0.172 in the MD and NMR, respectively. This agreement shows that the applied lipid force field accurately describes the configurational sampling of the lipids in the bilayer. Similar close agreements have been previously reported in numerous simulation studies for various lipid species.70 For the simulated nanodisc, the carbon atoms close to the membrane−water interface have slightly lower order parameters than those in the periodic bilayer. Nevertheless, averaged over the entire acyl chain, SCH is 0.188 for the ND and thus higher than that for the simulated periodic bilayer. Thus, the simulations correctly capture the trend of increased acyl chain order and lower entropy in NDs. However, SCH in the simulated ND is lower than that in the NMR experiments, in which SCH = 0.260. Although this disparity between simulated and experimental order parameters is pronounced, it corresponds to an inclination deviation of less than 5°. The difference between SCH is largest for the carbon atoms close to the membrane−water interface, whose order parameters seem to be severely lower in the simulations than in the NMR (Figure 5a). One possible reason for this discrepancy could be that the nanodiscs (but not the liposomes) used for the NMR experiments were precipitated by hygroscopic polyethylene glycol,16 which could lead to increased order parameters, especially in the headgroup region. However, although this putative effect could have an influence, it probably can only partly explain the observed difference between measured and

Figure 5. SCH order parameter as a function of carbon position along the lipid acyl tail. (a) Comparison between the simulation and experiment. (b) The order parameter decreases radially from the center toward the outer rim of the nanodisc.

simulated SCH, and additional reasons cannot be ruled out a priori. Thus, we consider another possible reason: the lateral confinement of the lipids due to the scaffold proteins could be underestimated in our simulations. The available area per lipid, A/L, measures this confinement and strongly correlates with the lipid order parameters. Recent SANS experiments suggest an A/L of only 0.50 nm2 for the DMPC nanodisc at 37 °C,23 whereas previous SAXS measurements suggested larger mean surface areas of about 0.6 to 0.65 nm2 for DMPC above the gelto-liquid phase transition temperature of 29 °C.25 From our simulations, we estimate a mean surface area of 0.625 nm2 per DMPC in the ND (see below), which is thus in agreement with the SAXS data. Our all-atom simulation of a tensionless DMPC bilayer yields a comparable area per lipid of 0.61 nm2. This latter value is in excellent agreement with experimental data for liquid crystalline DMPC bilayers at 303 K,71,72 showing that the lipid force field by itself yields accurate lateral areas. Although we cannot fully resolve this issue here, we stress that reducing the circumference of the nanodisc, as determined by the conformation of the scaffold proteins, by only about 5−7% would be sufficient to bring the nanodisc area into agreement with the SANS estimate (see next paragraph). Alternatively, increasing the number of lipid molecules in the ND by 10% would have a similar effect. Interestingly, the number of DMPC in the ND reported in the SANS study is 170,23 slightly more than the 160 lipids originally reported1 and used in our simulations. To test our hypothesis that a larger lateral area corresponds to lower order parameters in the ND, we carried out an additional 200 ns all-atom MD simulation of a periodic DMPC bilayer at the low area per lipid of 0.50 nm2, as derived from SANS.23 During this simulation, the lateral area of the simulation box was kept constant, and only the z-dimension 6996


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The Journal of Physical Chemistry B was coupled to a 1 bar pressure bath. Indeed, the higher SCH of 0.289 obtained from this simulation (Figure 5a, red dashed curve) is in much better agreement with the NMR data for the ND (SCH = 0.260). Thus, we conclude that the area of our simulated ND is likely slightly too large, leading to lower order parameters than those observed experimentally. Since for the tensionless periodic bilayer the simulated and experimental SCH values agree very well (Figure 5), we speculate that the observation that our simulations at an area per lipid of 0.50 nm2 yield higher order parameters than those measured for the ND indicate that the actual area per lipid in the ND is larger than the 0.50 nm2 reported in the SANS study. Simple linear interpolation yields a rough estimate of 0.55 nm2. Figure 5b shows how SCH changes as a function of the radial position of the lipids in the ND. Lipids at the center of the ND are significantly more ordered than annular lipids that are in contact with the scaffold proteins. A similar dependence on the position of the lipids in the ND has also been reported from short (200 ps to 10 ns) simulations of palmitoyloleoylphosphatidylcholine (POPC) containing NDs of different size.32,34 The radial dependence of the order parameters highlight the pronounced effect of MSP1Δ on the lipids. By tightly wrapping themselves around the edge of the nanodisc, the scaffold proteins on the one hand constrict the lipids and confine their motions. On the other hand, the packing of the annular lipids is perturbed due to the presence of the MSP1Δ surface. As a result, the overall constrictive effect, which is exerted from the outer rim of the ND, increases toward the center of the ND and leads to significantly different properties of the central lipids as compared to the annular ones. This lateral heterogeneity may also lead to a radial change in the lateral pressure profile across the ND membrane; testing this hypothesis is beyond the scope of the present work, however. Figure 6 compares the order parameters obtained from the AA and CG simulations. Figure 6a shows that AA and CG models not only yield comparable order parameters but also a similar dependence on the position in the ND. At the CG level, the average P2 (averaged over all bonds from both hydrocarbon tails) is 0.58, 0.41, and 0.27 for the central, middle, and annular lipids, respectively. These order parameters can be compared to the corresponding values of 0.61, 0.45, and 0.21 at the AA level. The largest and most systematic difference between AA and CG order parameters is observed for the bond between the phosphate headgroup and the ester group (bond nr. 2), which has a significantly lower order parameter at the AA level. A similar result is found for the periodic bilayer (Figure 6b). A peculiarity of the Martini-CG lipid force field is that the mapping of AA particles to CG beads is not strictly defined. For example, the DMPC model, comprising 10 CG beads (Figure 6b, inset), effectively represents all saturated PC lipids with acyl tails of 12−15 carbon atoms. Thus, there is some ambiguity involved in the AA/CG mapping. To investigate the effect on P2 of slightly different choices for the AA/CG mapping, we compared different assignments (see Table S1 in Supporting Information). However, the influence on P2 is very minor (Figure 6b). In summary, the lipid order parameters confirm the agreement between the AA and CG results. On average, the order parameters in the nanodisc are higher than those in the periodic bilayer, with the major contribution coming from the highly ordered lipids located at the center of the nanodisc. The order parameters obtained from our MD simulations are somewhat lower than those from NMR, which we assign to the

Figure 6. P2 order parameter for consecutive bonds in DMPC molecules for the (a) nanodisc and (b) bilayer. The solid and dashdotted lines denote the order parameters from the CG and AA simulations, respectively. The inset in b shows a CG DMPC lipid with corresponding bond numbers.

slightly overestimated lateral area of the ND in the MD simulations. Lateral Structure. To compare the lateral structure of the ND and the periodic bilayer, Figure 7 shows the radial distribution function (RDF) of the lipid headgroups in the bilayer plane. The first two peaks are located at the same distance in the ND and in the periodic bilayer. When comparing AA and CG RDFs, it is evident that the positions of the first two peaks are the same at both levels of resolution, indicating that the Martini-CG force field captures the

Figure 7. Lateral radial distribution function (RDF) of lipid headgroups (phosphate beads) in a nanodisc and bilayer from CG and AA simulations. 6997


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carbon atoms and the oxygen atoms of the glycerol ester groups. The distributions of the terminal methyl carbons (black lines) are similar for the central and annular lipids. However, the oxygen densities (red lines) reveal that the annular lipids form a significantly thinner bilayer, with a peak-to-peak distance of only 2.25 nm, as compared to 3.10 nm for the central lipids. Consequently, for the annular lipids, the carbon and oxygen density distributions overlap. Thus, the terminal methyl groups of the annular lipids are in closer proximity to the hydrated headgroup region, leading to the observed increased number of water contacts due to water penetration at the ND edges. Slow-down of Lateral Dynamics in Nanodiscs. The MSD of lipid molecules in the membrane plane provide insight into the lateral dynamics. As can be seen from Figure 10a, the

excluded-volume and local packing of the lipids very well. However, for both the periodic bilayer as well as the ND, the CG RDF is considerably more structured than that at the AA level, indicating a more pronounced and longer-ranged lateral order. This overstructuring has also been reported in neat CG liquids, such as water or alkanes.67,73,74 A possible remedy could be the use of softer repulsion potentials (softer than r−12). Water Penetration at Nanodisc Edges. Handa and coworkers23 measured the fluorescence lifetime of a (9anthroyloxy)-stearic acid (AS) probe located at different positions along the DMPC acyl tail. Although they found that in general, the fluorescence lifetime is longer in NDs than in LUVs, they also observed that for an AS probe attached close to the terminus of the acyl tail, the lifetimes in NDs and LUVs are similar. Since AS fluorescence is quenched by water, this finding suggests that in the ND, despite the overall tighter packing and decreased water contact frequency, the lipids located at the edges of the ND are more likely to be in contact with water.23 To test this hypothesis, we counted the number of water contacts of the terminal methyl carbon atoms in the DMPC acyl tails, as observed during the all-atom simulation. Figure 8 shows that indeed, water contacts of the terminal

Figure 8. Number of contacts (per lipid) between water and terminal methyl carbons for central (black) and annular (cyan) DMPC molecules in a nanodisc. A contact was counted if the terminal carbon was within 0.6 nm of a water oxygen atom. Data were averaged over both acyl tails.

methyl groups of the annular lipids are significantly more likely than for the lipids at the center of the ND. To further analyze the origin of this effect, Figure 9 shows the density distributions (along the bilayer normal) of the DMPC terminal methyl

Figure 10. (a) Lateral mean square displacement of lipids. Taking an MSD of 1 nm2 (roughly the lateral size of a single lipid) as a reference for illustration, diffusion in the nanodisc (black lines) is 18 times faster at the CG (dashed) than at the AA level (solid line), whereas this speed-up is only a factor 8 for the lamellar periodic bilayer (red lines). (b) Anomalous diffusion exponent.

confinement of the scaffold proteins slows down the translational motions of the lipids in the ND (black curves) as compared to the periodic bilayer (red curves). This effect is observed both at the AA and CG levels and is present already at short time intervals. In other words, the lipids are affected by the confinement even in their short time scale motions. To further characterize this diffusion retardation, we analyzed the nonlinear dependence of the MSD on time, MSD ∝ tα, by calculating the time exponent α. Normal (free) diffusion is characterized by α = 1, whereas α < 1 indicates the subdiffusive regime. Figure 10b shows that in the periodic bilayer, α converges to 1 for t > 10 ns, which corresponds to the time it takes for a lipid to diffuse about its own diameter and thus escape from the cage of neighboring lipids. By contrast, in the ND, this free diffusion regime is never reached. Already the

Figure 9. Density distributions along the bilayer normal for (a) annular and (b) central DMPC molecules in a nanodisc. The density distribution of the terminal methyl carbons and the ester oxygens are shown in black and red, respectively. 6998


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in our simulations, are in agreement with experimental findings16 and suggest that the lipid environment experienced by a membrane protein embedded in a nanodisc might be more tightly packed and viscous. This could alter the structure and/ or dynamics of the membrane protein. Indeed, solid-state NMR experiments of Glaubitz and co-workers revealed slightly altered properties of green proteorhodopsin in terms of photocycle and molecular dynamics.16 It is, however, difficult to disentangle whether the observed effects are caused by the altered oligomeric state within NDs or by the higher lipid order parameter or by both. Our simulations show that the increased lipid order, which has also been reported for DMPC-containing lipodiscs in which lipid patches are surrounded by polymers,77 is due to the constriction exerted by the scaffold proteins from the outer rim of the ND and radially increasing toward its center. As a consequence, lipids located at the center of the ND are significantly more ordered, whereas the opposite is the case for the annular lipids that are in direct contact with the scaffold proteins, which are highly disordered due to perturbed packing. Nevertheless, on average, lipid order is increased in NDs as compared to the conventional lamellar bilayer phase. The higher degree of disorder of the annular lipids is accompanied by an increased number of water contacts of the terminal methyl groups due to backfolding of the acyl tails into the headgroup region and water penetration at the edges of the nanodisc, consistent with fluorescence data.23 The nanodisc and periodic bilayer have a similar lateral lipid structure, indicated by the comparable radial distribution functions of the lipid headgroups in the bilayer plane. However, at the CG level, the lateral structure is significantly longerranged than in the all-atom simulations. Interestingly, this overstructuring does not slow down the lateral dynamics, on the contrary. Compared to the all-atom simulations, the lateral mean-square displacements of the lipids in the CG-MD simulations are higher by a factor of 8 and 18 for the periodic bilayer and the nanodisc, respectively. Thus, although the same lipids (DMPC) are present in both systems, different time scaling factors have to be applied to convert the CG-MD simulation time to a realistic time scale that would be comparable to experimental data. In the present work, we did not attempt to scale times and report plain CG-MD simulation times. Although the present work also highlights some of the limitations of the CG-Martini force field, e.g., the underestimated entropy difference between nanodisc and bilayer DMPC lipids or the necessity to impose a helical structure on MSP1Δ, the CG-MD results are overall very promising. The CG-MD simulations enable the spontaneous self-assembly of lipids and scaffold proteins into a stable nanodisc on the multimicrosecond time scale and to obtain a statistically converged structural ensemble of an equilibrated nanodisc. The latter was used as a starting point for subsequent simulations at the fully atomistic level, which validated the CG results and enabled a direct and quantitative comparison to the experiments. Successful application of this dual-scale allatom/CG approach opens the way for further studies of nanodisc systems, also including embedded membrane proteins. For example, it could be feasible to incorporate a membrane protein into a nanodisc by carrying out the selfassembly simulations in the presence of a membrane protein. Such simulations could help to address the open question as to why some membrane proteins get readily incorporated into nanodiscs and others do not.

local translational motions on short time scales are hindered by the scaffold proteins, and in the long time limit, in which the lipids explore the entire (limited) available area, diffusion is affected by the global confinement due to the scaffolding (the long time regime is only captured in the CG-MD simulations, dashed curves). The interplay between the local effect (decreasing with increasing time interval) and the global effect (increasing with time) leads to the observed maximum in α, which is reached before α approaches 1. The lateral dynamics in the AA simulations is qualitatively similar to the CG level but suffers from poor sampling in the long time limit (Figure 10b). In the CG-MD simulation of the ND, the MSD reaches a plateau value after ca. 400 ns, indicating complete sampling of the available area. By solving the two-dimensional diffusion equation along with reflecting boundary conditions at the circumference of the nanodisc, the MSD can be approximated 2 by ⟨(r(t) − r(t0))2⟩ ≈ R2[1−e(−a(t−t0)/R )], where lipids are assumed to freely diffuse inside a disc of radius R.31 We obtained R = 3.99 nm after fitting the MSD of our CG-MD simulation to the above equation. Hence, the average area available for each DMPC lipid in the ND is πR2/80 = 0.625 nm2, which is similar to the area per lipid found in our simulations of the tensionless periodic bilayer (see above). In addition, the lateral diffusion may be used to gauge the time scales of the CG and AA simulations. In the CG-Martini force field, lipid diffusion is faster than that at the AA level because the reduced friction from the missing atomistic degrees of freedom smoothens the CG energy landscape.50 To take this effect into account, CG-MD simulation times have often been scaled in previous studies, ideally by comparing to experimental or all-atom simulation data. In general, the time scaling factor is not easily predictable, as it may vary with the composition and state point of a system.75,76 Figure 10a shows that the speed-up in the CG-MD simulations over the all-atom MD is different in the ND and the periodic bilayer. Taking an MSD of 1 nm2 as a reference, we see that in the ND, lipid diffusion is about 18 times faster at the CG than at the AA level, whereas only an 8fold increase is found for the periodic bilayer system, although both systems comprise the same lipid species. This result demonstrates that for every system, a careful calibration has to be carried out before time scales from CG-MD simulations can be translated into realistic time scales that can be compared to experiments.

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SUMMARY AND CONCLUSIONS

In this work, we have combined all-atom- and CG-MD simulations to study the structural and dynamical properties of phospholipid nanodiscs on long time scales. We have focused on empty nanodiscs comprising DMPC lipids, enabling a direct and quantitative comparison not only between all-atom and CG levels of resolution, which is invaluable for assessing the suitability of computationally efficient CG simulations for future studies of nanodisc systems, but also between our simulations and recent experimental data on the same system.16,23 We found that lipid acyl tail configurational entropies are lower and that order parameters are higher in the nanodisc than in a conventional periodic bilayer. Consistent results were obtained at both AA and CG levels, showing that the applied CG-Martini force field can, at least qualitatively, capture the differences between the configurational ensembles in NDs and conventional periodic bilayers. The higher lipid order parameters in NDs, although somewhat underestimated 6999


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grant to L.S.). The Research Department Interfacial Systems Chemistry (IFSC) of the Ruhr-University Bochum is thankfully acknowledged.

Concerning the lipid environment experienced by a membrane protein in a nanodisc, our present study as well as previous experimental data indicate that the lipids in the nanodisc are more ordered than those in a conventional bilayer. This could alter the structure and/or dynamics of the membrane protein. However, one has to be cautious upon transferring results obtained for an empty nanodisc to a nanodisc loaded with a protein. For example, recent work of Eggensperger and co-workers,39 who incorporated a dimeric ABC transporter into a nanodisc comprising E. coli polar lipids, showed that the membrane protein replaced a considerably larger number of lipids from the nanodisc than expected purely geometrically from the cross-sectional area of its transmembrane domain. All-atom MD simulations showed that even as little as 22 lipids, as determined experimentally, sufficed to form an annular belt around the ABC transporter and isolate it from the MSP scaffold.39 To do that, the lipids adopted highly disordered and tilted configurations to cover the hydrophobic surface of the ABC transporter. At the same time, also the scaffold proteins were less helical to adapt the shape of the ND. In such situations, the assumption of fully helical MSP1Δ proteins underlying the CG-MD approach would not be valid. The study of Eggensperger and co-workers thus shows that the presence of a membrane protein can alter the affinity of the system toward lipids and hence the stoichiometry of the final membrane protein−nanodisc complex, which can in turn alter the lipid properties. A key result of the present study is the lower entropy of the lipids in the nanodisc, which is in agreement with the increased acyl tail order parameters. Clearly, entropy and order parameters are expected to be closely related, with higher order parameters corresponding to lower entropies and vice versa. Indeed, for proteins, a quantitative relationship between differences in NMR-derived generalized (Lipary-Szabo) S2 order parameters and conformational entropies has been established, and entropy-meters have been empirically calibrated.78−83 To the best of our knowledge, a corresponding quantitative link between lipid SCH order parameters and entropy has not yet been established. Based on extended and systematic studies over a wide range of order parameters and different lipid species, MD simulations could help to close this gap.

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(1) Denisov, I. G.; Grinkova, Y. V.; Lazarides, A. A.; Sligar, S. G. Directed self-assembly of monodisperse phospholipid bilayer nanodiscs with controlled size. J. Am. Chem. Soc. 2004, 126, 3477−3487. (2) Nath, A.; Atkins, W. M.; Sligar, S. G. Applications of phospholipid bilayer nanodiscs in the study of membranes and membrane proteins. Biochemistry 2007, 46, 2059−2069. (3) Bayburt, T. H.; Sligar, S. G. Membrane protein assembly into nanodiscs. FEBS Lett. 2010, 584, 1721−1727. (4) Borch, J.; Hamann, T. The nanodisc: a novel tool for membrane protein studies. Biol. Chem. 2009, 390, 805−814. (5) Popot, J.-L. Amphipols, nanodiscs, and fluorinated surfactants: three nonconventional approaches to studying membrane proteins in aqueous solutions. Annu. Rev. Biochem. 2010, 79, 737−775. (6) Lee, A. G. Lipid-protein interactions in biological membranes: a structural perspective. Biochim. Biophys. Acta 2003, 1612, 1−40. (7) Seddon, A. M.; Curnow, P.; Booth, P. J. Membrane proteins, lipids and detergents: not just a soap opera. Biochim. Biophys. Acta 2004, 1666, 105−117. (8) Linke, D. Detergents: an overview. Methods Enzymol. 2009, 463, 603−617. (9) Katayama, H.; Wang, J.; Tama, F.; Chollet, L.; Gogol, E. P.; Collier, R. J.; Fisher, M. T. Three-dimensional structure of the anthrax toxin pore inserted into lipid nanodiscs and lipid vesicles. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 3453−3457. (10) Frauenfeld, J.; Gumbart, J.; van der Sluis, E. O.; Funes, S.; Gartmann, M.; Beatrix, B.; Mielke, T.; Berninghausen, O.; Becker, T.; Schulten, K.; et al. Cryo-EM structure of the ribosome-SecYE complex in the membrane environment. Nat. Struct. Mol. Biol. 2011, 18, 614− 621. (11) Raschle, T.; Hiller, S.; Yu, T.-Y.; Rice, A. J.; Walz, T.; Wagner, G. Structural and functional characterization of the integral membrane protein VDAC-1 in lipid bilayer nanodiscs. J. Am. Chem. Soc. 2009, 131, 17777−17779. (12) Hagn, F.; Etzkorn, M.; Raschle, T.; Wagner, G. Optimized phospholipid bilayer nanodiscs facilitate high-resolution structure determination of membrane proteins. J. Am. Chem. Soc. 2013, 135, 1919−1925. (13) Li, Y.; Kijac, A. Z.; Sligar, S. G.; Rienstra, C. M. Structural analysis of nanoscale self-assembled discoidal lipid bilayers by solidstate NMR spectroscopy. Biophys. J. 2006, 91, 3819−3828. (14) Kijac, A. Z.; Li, Y.; Sligar, S. G.; Rienstra, C. M. Magic-angle spinning solid-state NMR spectroscopy of nanodisc-embedded human CYP3A4. Biochemistry 2007, 46, 13696−13703. (15) Kijac, A.; Shih, A. Y.; Nieuwkoop, A. J.; Schulten, K.; Sligar, S. G.; Rienstra, C. M. Lipid-protein correlations in nanoscale phospholipid bilayers determined by solid-state nuclear magnetic resonance. Biochemistry 2010, 49, 9190−9198. (16) Mörs, K.; Roos, C.; Scholz, F.; Wachtveitl, J.; Dötsch, V.; Bernhard, F.; Glaubitz, C. Modified lipid and protein dynamics in nanodiscs. Biochim. Biophys. Acta 2013, 1828, 1222−1229. (17) Boldog, T.; Grimme, S.; Li, M.; Sligar, S.; Hazelbauer, G. Nanodiscs separate chemoreceptor oligomeric states and reveal their signaling properties. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 11509− 11514. (18) Bayburt, T.; Leitz, A.; Xie, G.; Oprian, D.; Sligar, S. Transducin activation by nanoscale lipid bilayers containing one and two rhodopsins. J. Biol. Chem. 2007, 282, 14875−14881. (19) Tsukamoto, H.; Sinha, A.; DeWitt, M.; Farrens, D. Monomeric rhodopsin is the minimal functional unit required for arrestin binding. J. Mol. Biol. 2010, 399, 501−511. (20) Bayburt, T.; Vishnivetskiy, S.; McLean, M.; Morizumi, T.; Huang, C.; Tesmer, J.; Ernst, O.; Sligar, S.; Gurevich, V. Monomeric rhodopsin is sufficient for normal rhodopsin kinase (GRK1)

ASSOCIATED CONTENT

S Supporting Information *

Different AA/CG mapping schemes (Figure 6b). The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b02101.

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*(A.D.) Phone: +91 291 244 9026 E-mail: [email protected]. *(L.V.S.) Phone: +49 234 3221582. Fax: +49 234 3214045. Email: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Clemens Glaubitz, Srinivasa Gopal, and Alex de Vries for carefully reading the manuscript and for helpful discussions. The German Research Foundation supported this work (Cluster of Excellence RESOLV (EXC 1069), Emmy Noether 7000


Article

The Journal of Physical Chemistry B phosphorylation and arrestin-1 binding. J. Biol. Chem. 2011, 286, 1420−1428. (21) Roos, C.; Zocher, M.; Müller, D.; Münch, D.; Schneider, T.; Sahl, H.-G.; Scholz, F.; Wachtveitl, J.; Ma, Y.; Proverbio, D.; et al. Characterization of co-translationally formed nanodisc complexes with small multidrug transporters, proteorhodopsin and with the E. coli MraY translocase. Biochim. Biophys. Acta 2012, 1818, 3098−3106. (22) Fischer, N. O.; Weilhammer, D.; Dunkle, A.; Thomas, C.; Hwang, M.; Corzett, M.; Lychak, C.; Mayer, W.; Urbin, S.; Collette, N.; et al. Evaluation of nanolipoprotein particles (NLPs) as an in vivo delivery platform. PLoS One 2014, 9, e93342. (23) Nakano, M.; Fukuda, M.; Kudo, T.; Miyazaki, M.; Wada, Y.; Matsuzaki, N.; Endo, H.; Handa, T. Static and dynamic properties of phospholipid bilayer nanodiscs. J. Am. Chem. Soc. 2009, 131, 8308− 8312. (24) Shaw, A. W.; McLean, M. A.; Sligar, S. G. Phospholipid phase transitions in homogeneous nanometer scale bilayer discs. FEBS Lett. 2004, 556, 260−264. (25) Denisov, I. G.; McLean, M. A.; Shaw, A. W.; Grinkova, Y. V.; Sligar, S. G. Thermotropic phase transition in soluble nanoscale lipid bilayers. J. Phys. Chem. B 2005, 109, 15580−15588. (26) Gumbart, J.; Wang, Y.; Aksimentiev, A.; Tajkhorshid, E.; Schulten, K. Molecular dynamics simulations of proteins in lipid bilayers. Curr. Opin. Struct. Biol. 2005, 15, 423−431. (27) Lindahl, E.; Sansom, M. S. P. Membrane proteins: molecular dynamcis simulations. Curr. Opin. Struct. Biol. 2008, 18, 425−431. (28) Marrink, S. J.; de Vries, A. H.; Tieleman, D. P. Lipids on the move: Simulations of membrane pores, domains, stalks and curves. Biochim. Biophys. Acta 2009, 1788, 149−168. (29) Segrest, J. P.; Jones, M. K.; Klon, A. E.; Sheldahl, C. J.; Hellinger, M.; De Loof, H.; Harvey, S. C. A detailed molecular belt model for apolipoprotein A-I in discoidal high density lipoprotein. J. Biol. Chem. 1999, 274, 31755−31758. (30) Klon, A. E.; Segrest, J. P.; Harvey, S. C. Molecular dynamics simulations on discoidal HDL particles suggest a mechanism for rotation in the apo A-I belt model. J. Mol. Biol. 2002, 324, 703−721. (31) Shih, A. Y.; Denisov, I. G.; Phillips, J. C.; Sligar, S. G.; Schulten, K. Molecular dynamics simulations of discoidal bilayers assembled from truncated human lipoproteins. Biophys. J. 2005, 88, 548−556. (32) Catte, A.; Patterson, J. C.; Jones, M. K.; Jerome, W. G.; Bashtovyy, D.; Su, Z.; Gu, F.; Chen, J.; Aliste, M. P.; Harvey, S. C.; et al. Novel changes in discoidal high density lipoprotein morphology: a molecular dynamics study. Biophys. J. 2006, 90, 4345−4360. (33) Shih, A. Y.; Sligar, S. G.; Schulten, K. Molecular models need to be tested: the case of a solar flares discoidal HDL model. Biophys. J. 2008, 94, L87−L89. (34) Jones, M. K.; Catte, A.; Patterson, J. C.; Gu, F.; Chen, J.; Li, L.; Segrest, J. P. Thermal stability of apolipoprotein A-I in high-density lipoproteins by molecular dynamics. Biophys. J. 2009, 96, 354−371. (35) Gu, F.; Jones, M. K.; Chen, J.; Patterson, J. C.; Catte, A.; Jerome, W. G.; Li, L.; Segrest, J. P. Structures of discoidal high density lipoproteins: a combined computational-experimental approach. J. Biol. Chem. 2010, 285, 4652−4665. (36) Jones, M. K.; Zhang, L.; Catte, A.; Li, L.; Oda, M. N.; Ren, G.; Segrest, J. P. Assessment of the validity of the double superhelix model for reconstituted high density lipoproteins: a combined computationalexperimental approach. J. Biol. Chem. 2010, 285, 41161−41171. (37) Jones, M. K.; Zhang, L.; Catte, A.; Li, L.; Oda, M. N.; Ren, G.; Segrest, J. P. “Sticky” and ”promiscuous”, the yin and yang of apolipoprotein A-I termini in discoidal high-density lipoproteins: a combined computational-experimental approach. Biochemistry 2011, 50, 2249−2263. (38) Segrest, J. P.; Jones, M. K.; Catte, A.; Thirumuruganandham, S. P. Validation of previous computer models and MD simulations of discoidal HDL by a recent crystal structure of apoA-I. J. Lipid Res. 2012, 53, 1851−1863. (39) Eggensperger, S.; Fisette, O.; Parcej, D.; Schäfer, L. V.; Tampé, R. An annular lipid belt is essential for allosteric coupling and viral inhibition of the antigen translocation complex TAP (transporter

associated with antigen processing). J. Biol. Chem. 2014, 289, 33098− 33108. (40) Shih, A. Y.; Arkhipov, A.; Freddolino, P. L.; Schulten, K. A coarse grained protein-lipid model with application to lipoprotein particles. J. Phys. Chem. B 2006, 110, 3074−3084. (41) Shih, A. Y.; Freddolino, P. L.; Arkhipov, A.; Schulten, K. Assembly of lipoprotein particles revealed by coarse-grained molecular dynamics simulations. J. Struct. Biol. 2007, 157, 579−592. (42) Shih, A. Y.; Arkhipov, A.; Freddolino, P. L.; Sligar, S. G.; Schulten, K. Assembly of lipids and proteins into lipoprotein particles. J. Phys. Chem. B 2007, 111, 11095−11104. (43) Peter, C.; Kremer, K. Multiscale simulation of soft matter systems - from the atomistic to the coarse-grained level and back. Soft Matter 2009, 5, 4357−4366. (44) Catte, A.; Patterson, J. C.; Bashtovyy, D.; Jones, M. K.; Gu, F.; Li, L.; Rampioni, A.; Sengupta, D.; Vuorela, T.; Niemelä, P.; et al. Structure of spheroidal HDL particles revealed by combined atomistic and coarse-grained simulations. Biophys. J. 2008, 94, 2306−2319. (45) Shih, A. Y.; Sligar, S. G.; Schulten, K. Maturation of high-density lipoproteins. J. R. Soc. Int. 2009, 6, 863−871. (46) Koivuniemi, A.; Heikelä, M.; Kovanen, P. T.; Vattulainen, I.; Hyvönen, M. T. Atomistic simulations of phosphatidylcholines and cholesteryl esters in high-density lipoprotein-sized lipid droplet and trilayer: clues to cholesteryl ester transport and storage. Biophys. J. 2009, 96, 4099−4108. (47) Gogonea, V.; Wu, Z.; Lee, X.; Pipich, V.; Li, X.-M.; Ioffe, A. I.; Didonato, J. A.; Hazen, S. L. Congruency between biophysical data from multiple platforms and molecular dynamics simulation of the double-super helix model of nascent high-density lipoprotein. Biochemistry 2010, 49, 7323−7343. (48) Vuorela, T.; Catte, A.; Niemelä, P. S.; Hall, A.; Hyvönen, M. T.; Marrink, S.-J.; Karttunen, M.; Vattulainen, I. Role of lipids in spheroidal high density lipoproteins. PLoS Comput. Biol. 2010, 6, e1000964. (49) Yetukuri, L.; Söderlund, S.; Koivuniemi, A.; Seppänen-Laakso, T.; Niemelä, P. S.; Hyvönen, M.; Taskinen, M.-R.; Vattulainen, I.; Jauhiainen, M.; Oresic, M. Composition and lipid spatial distribution of HDL particles in subjects with low and high HDL-cholesterol. J. Lipid Res. 2010, 51, 2341−2351. (50) Marrink, S. J.; Risselada, H. J.; Yefimov, S.; Tieleman, D. P.; de Vries, A. H. The MARTINI force field: coarse grained model for biomolecular simulations. J. Phys. Chem. B 2007, 111, 7812−7824. (51) Monticelli, L.; Kandasamy, S. K.; Periole, X.; Larson, R. G.; Tieleman, D. P.; Marrink, S. J. The MARTINI coarse-grained force field: extension to proteins. J. Chem. Theory Comput. 2008, 4, 819− 834. (52) de Jong, D. H.; Singh, G.; Bennett, W. F. D.; Arnarez, C.; Wassenaar, T. A.; Schäfer, L. V.; Periole, X.; Tieleman, D. P.; Marrink, S. J. Improved parameters for the Martini coarse-grained protein force field. J. Chem. Theory Comput. 2013, 9, 687−697. (53) Borhani, D. W.; Rogers, D. P.; Engler, J. A.; Brouillette, C. G. Crystal structure of truncated human apolipoprotein A-I suggests a lipid-bound conformation. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 12291−12296. (54) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: algorithms for highly efficient, load-balanced, and scalable molecular simulation. J. Chem. Theory Comput. 2008, 4, 435−447. (55) Bussi, G.; Donadio, D.; Parrinello, M. Canonical sampling through velocity rescaling. J. Chem. Phys. 2007, 126, 014101. (56) Rzepiela, A. J.; Schäfer, L. V.; Goga, N.; Risselada, H. J.; de Vries, A. H.; Marrink, S. J. Reconstruction of atomistic details from coarse-grained structures. J. Comput. Chem. 2010, 31, 1333−1343. (57) Schuler, L. D.; van Gunsteren, W. F. On the choice of dihedral angle potential energy functions for n-alkanes. Mol. Simulation 2000, 25, 301−319. (58) Berger, O.; Edholm, O.; Jähnig, F. Molecular dynamics simulations of a fluid bilayer of dipalmitoylphosphatidylcholine at full hydration, constant pressure, and constant temperature. Biophys. J. 1997, 72, 2002−2013. 7001


Article


order parameters: application to protein folding. J. Mol. Biol. 1996, 263, 369−382. (80) Li, Z.; Raychaudhuri, S.; Wand, A. J. Insights into the local residual entropy of proteins provided by NMR relaxation. Protein Sci. 1996, 5, 2647−2650. (81) Frederick, K. K.; Marlow, M. S.; Valentine, K. G.; Wand, A. J. Conformational entropy in molecular recognition by proteins. Nature 2007, 448, 325−329. (82) Marlow, M. S.; Dogan, J.; Frederick, K. K.; Valentine, K. G.; Wand, A. J. The role of conformational entropy in molecular recognition by calmodulin. Nat. Chem. Biol. 2010, 6, 352−358. (83) Tzeng, S.-R.; Kalodimos, C. G. Protein activity regulation by conformational entropy. Nature 2012, 488, 236−240. (84) Kabsch, W.; Sander, C. Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features. Biopolymers 1983, 22, 2577−2637.

(59) Hornak, V.; Abel, R.; Okur, A.; Strockbine, B.; Roitberg, A.; Simmerling, C. Comparison of multiple Amber force fields and development of improved protein backbone parameters. Proteins 2006, 65, 712−725. (60) Lindorff-Larsen, K.; Piana, S.; Palmo, K.; Maragakis, P.; Klepeis, J. L.; Dror, R. O.; Shaw, D. E. Improved side-chain torsion potentials for the Amber ff99SB protein force field. Proteins 2010, 78, 1950− 1958. (61) Cordomi, A.; Caltabiano, G.; Pardo, L. Membrane protein simulations using Amber force field and Berger lipid parameters. J. Chem. Theory Comput. 2012, 8, 948−958. (62) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 1983, 79, 926−935. (63) Miyamoto, S.; Kollman, P. A. SETTLE: An analytical version of the SHAKE and RATTLE algorithm for rigid water models. J. Comput. Chem. 1992, 13, 952−962. (64) Hess, B. P-LINCS: a parallel linear constraint solver for molecular simulation. J. Chem. Theory Comput. 2008, 4, 116−122. (65) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. A smooth particle mesh Ewald method. J. Chem. Phys. 1995, 103, 8577. (66) Schlitter, J. Estimation of absolute and relative entropies of macromolecules using the covariance matrix. Chem. Phys. Lett. 1993, 215, 617−621. (67) Baron, R.; de Vries, A. H.; Hünenberger, P. H.; van Gunsteren, W. F. Comparison of atomic-level and coarse-grained models for liquid hydrocarbons from molecular dynamics configurational entropy estimates. J. Phys. Chem. B 2006, 110, 8464−8473. (68) Baron, R.; de Vries, A. H.; Hünenberger, P. H.; van Gunsteren, W. F. Configurational entropies of lipids in pure and mixed bilayers from atomic-level and coarse-grained molecular dynamics simulations. J. Phys. Chem. B 2006, 110, 15602−15614. (69) Mei, X.; Atkinson, D. Crystal structure of C-terminal truncated apolipoprotein A-I reveals the assembly of high density lipoprotein (HDL) by dimerization. J. Biol. Chem. 2011, 286, 38570−38582. (70) Vermeer, L. S.; de Groot, B. L.; Réat, V.; Milon, A.; Czaplicki, J. Acyl chain order parameter profiles in phospholipid bilayers: computation from molecular dynamics simulations and comparison with 2H NMR experiments. Eur. Biophys. J. 2007, 36, 919−931. (71) Petrache, H. I.; Dodd, S. W.; Brown, M. F. Area per lipid and acyl length distributions in fluid phosphatidylcholines determined by 2H NMR spectroscopy. Biophys. J. 2000, 79, 3172−3192. (72) Kucerka, N.; Liu, Y.; Chu, N.; Petrache, H. I.; Tristram-Nagle, S.; Nagle, J. F. Structure of fully hydrated fluid phase DMPC and DLPC lipid bilayers using X-ray scattering from oriented multilamellar arrays and from unilamellar vesicles. Biophys. J. 2005, 88, 2626−2637. (73) He, X.; Shinoda, W.; DeVane, R.; Klein, M. L. Exploring the utility of coarse-grained water models for computational studies of interfacial systems. Mol. Phys. 2010, 108, 2007−2020. (74) Chiu, S.-W.; Scott, H. L.; Jakobsson, E. A coarse-grained model based on morse potential for water and n-alkanes. J. Chem. Theory Comput. 2010, 6, 851−863. (75) Fritz, D.; Koschke, K.; Harmandaris, V. A.; van der Vegt, N. F. A.; Kremer, K. Multiscale modeling of soft matter: scaling of dynamics. Phys. Chem. Chem. Phys. 2011, 13, 10412−10420. (76) Marrink, S. J.; Tieleman, D. P. Perspective on the Martini model. Chem. Soc. Rev. 2013, 42, 6801−6822. (77) Orwick, M. C.; Judge, P. J.; Procek, J.; Lindholm, L.; Graziadei, A.; Engel, A.; Gröbner, G.; Watts, A. Detergent-free formation and physicochemical characterization of nanosized lipid-polymer complexes: Lipodisq. Angew. Chem., Int. Ed. 2012, 51, 4653−4657. (78) Akke, M.; Brüschweiler, R.; Palmer, A. G. NMR order parameters and free energy: an analytical approach and its application to cooperative calcium (2+) binding by calbindin D9k. J. Am. Chem. Soc. 1993, 115, 9832−9833. (79) Yang, D.; Kay, L. E. Contributions to conformational entropy arising from bond vector fluctuations measured from NMR-derived 7002


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